Step-by-step explanation:
Simplify the expression \sqrt{x^{2}+12}- \sqrt{12}.
Write the expression as a product where the root of one of the factors can be evaluated.
sqrt(x ^ 2 + 12) - sqrt(4 * 3)
Write the expression in exponential form with the base 2.
sqrt(x ^ 2 + 12) - sqrt(2 ^ 2 * 3)
Use the property that the root of a product is equal to the product of the roots of each factor.
sqrt(x ^ 2 + 12) - sqrt(2 ^ 2) * sqrt(3)
Take the square root of 2 ^ 2
sqrt(x ^ 2 + 12) - 2sqrt(3)
Substitute x = 0 into the simplified expression.
sqrt(x ^ 2 + 12) - 2sqrt(3)
sqrt(0 ^ 2 + 12) - 2sqrt(3)
Simplify the expression.
0
Solution
The limit is 0.
